Euclid’s Random Walk: Simulation as a tool for geometric reasoning through development

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Description: Geometry has formed the foundation of architecture, science, and technology for millennia, yet the mental representations and processes that guide human geometric reasoning through development are not well understood. The present study explores the changing role of dynamic mental simulations in human reasoning about the properties of static, immutable geometric objects, like triangles. One-hundred-twenty-five 7-12-year-old children and 30 adults completed a reasoning task about the general properties of triangles and a simulation task for completing fragmented triangles. While basic Euclidean principles guided even young children’s simulations, only older children and adults reasoned successfully about triangle properties. Successful geometric reasoning may emerge when children abandon incorrect, axiomatic-based strategies and come to rely on simulations, which provide relatively robust information about the distance and angle properties of triangles. While problems in geometry may seem answerable by immediate inference or by deductive proof, human geometric reasoning may instead rely on noisy, dynamic simulations.

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A child participating in the Reasoning Task. We suggest that successful geometric judgments may emerge when children begin to reason by dynamic mental simulations.

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